Deck 11: Infinite Sequences and Series

Question 1

Find the sum of the series.

Answer 1

Question 2

Determine whether the series is convergent or divergent.

Answer 2

converges

Question 3

Answer 3

Question 4

Question 5

Determine whether the series is convergent or divergent.

Question 6

Question 7

Determine whether the series converges or diverges.

Question 8

Find a formula for the general term of the sequence, assuming that the pattern of the first few
terms continues.

Question 9

Use the sum of the first 10 terms to approximate the sum of the series.Estimate the error.

Question 10

Determine whether the series is convergent or divergent.

Question 11

Test the series for convergence or divergence.

Question 12

Determine whether the series converges or diverges.

Question 13

Determine whether the given series converges or diverges.If it converges, find its sum.

Question 14

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of
values of x for which the given approximation is accurate to within the stated error.

Question 15

Test the series for convergence or divergence.

Question 16

Use the binomial series to expand the function as a power series.Find the radius of convergence.

Question 17

Question 18

Test the series for convergence or divergence.

Question 19

Test the series for convergence or divergence.

Question 20

Determine whether the given series is convergent or divergent.

Question 21

Question 22

Use series to evaluate the limit correct to three decimal places.

Question 23

Question 24

Question 25

Determine which one of the p-series below is divergent.

Question 26

Use series to approximate the definite integral to within the indicated accuracy.

Question 27

Question 28

____

Question 29

Which of the given series are absolutely convergent?

Question 30

Question 31

Find an approximation of the sum of the series accurate to two decimal places.

Question 32

Find a power series representation for

Question 33

Find the interval of convergence of the series.

Question 34

Question 35

Question 36

Approximate the sum to the indicated accuracy.

Question 37

Find the radius of convergence and the interval of convergence of the power series.

Question 38

Question 39

Question 40

Find the radius of convergence and the interval of convergence of the power series.

Question 41

Question 42

Determine whether the sequence convergent or divergent.

Question 43

Question 44

Question 45

Determine whether the geometric series converges or diverges.If it converges, find its sum.

Question 46

Test the series for convergence or divergence.

Question 47

Question 48

Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

Question 49

Question 50

Question 51

A rubber ball is dropped from a height of 8 m onto a flat surface.Each time the ball hits the surface, it rebounds to 50% of its previous height.Find the total distance the ball travels.

A)16
B)24
C)8
D)32

Question 52

Find the sum of the series.

Question 53

Find the value of the limit for the sequence given.

Question 54

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.

Question 55

Find the radius of convergence and the interval of convergence of the power series.

Question 56

Determine which series is convergent.

Question 57

Find the values of p for which the series is convergent.

Question 58

Determine whether the geometric series converges or diverges.If it converges, find its sum.

Question 59

Question 60

Find the radius of convergence and the interval of convergence of the power series.